Actually, there is not one, or two mistakes in the extension question. There are in fact three mistakes!

Miss Chavda, KSHS, Lincolnshire

Year 7s enjoyed this, and found a logical way to find all the solutions - 7A

Helsby High School, 9y4

Most of the class liked this. Thank you.

Amal, London

There are 24 ways.

N Cox, Ipswich

Great starter. Extended to four 5, 6 and 7 people and to the use of the factorial key on the calculator.

Angel, Sacred Heart High

There are 24 ways to stand in the straight line!

James, Weston

I really enjoyed this starter, because our class stood up and lined up for us to work out the answer :).

Mr Musker And Class 4, Warden Hill Junior School

We think that there are 24.

Year 8 Legends, King James's

We found 24 too. We also enjoyed doing the line-up.

Year 6 - Sir John Heron School, Newham

Nice starter. The children in y6 need another one to consolidate!

Mr Kavanagh's Fifth Class, Cork, Ireland

We figured out that if there were ten people in the line there would be 3,628,800 different ways to arrange them.

Transum,

Many people have said how much they enjoyed this activity. If you would like to move on to something related and something which the pupils can do on their computers, slates or iPads etc then try the Combinations and Permutations list of activities such as Ice Cream Combinations, Misfits and Striped Sweets. It will reinforce the idea of having a logical, well-ordered strategy for listing all the possibilities.

Mrs. Lorenzo,

This was an awesome problem to solve. My class roared with laughter at the sight of the characters - they add a fun dimension to the puzzle. Ashika got it right away. My grade 3 class did it. I was suprised at what the're capable of!

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Extension activities

Here is a solution to this problem with at least one mistake.Can you spot the mistake(s)?

In how many ways can 5, 10 or 100 people stand in line?

In how many different ways can the letters in the word Transum be arranged?

In how many different ways can the letters in the word Google be arranged?

Extension Answers

There are three mistakes (in arrangements 8, 14 and 20)

5! = 120

10! = 3,628,800

100! = 93,326,215,443,944,152,681,699,238,856,266,700,490,715,968,264,381,621,468,592,963,895,217,599,993,229,915,608,941,463,976,156,518,286,253,697,920,827,223,758,251,185,210,916,864,000,000,000,000,000,000,000,000(a number too big for most calculators but is approximately 9.33 x 10157).

The word Transum can be arranged in 7! = 5,040 ways

The word Google can be arranged in 6! ÷ (2! × 2!) = 180 ways (as it has two each of letters o and g).